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For which the value of f(x) = 2x^2 + 9 will be the same as g(x) = 3^x?

Sagot :

xero099

Answer:

For [tex]x = 3[/tex] the value of [tex]f(x) = 2\cdot x^{2}+9[/tex] will be the same of [tex]g(x) = 3^{x}[/tex].

Step-by-step explanation:

To determine for which value of [tex]x[/tex], we need to apply the following identity ([tex]f(x) = g(x)[/tex]) and solve numerically the resulting expression:

[tex]2\cdot x^{2}+9 = 3^{x}[/tex]

[tex]3^{x}-2\cdot x^{2}-9=0[/tex] (1)

A quick approach is using graphic tool and looking for the value of [tex]x[/tex] such that  [tex]3^{x}-2\cdot x^{2}-9=0[/tex]. The result of the analysis is included below in the attached image. We find the following result:

[tex]x = 3[/tex]

For [tex]x = 3[/tex] the value of [tex]f(x) = 2\cdot x^{2}+9[/tex] will be the same of [tex]g(x) = 3^{x}[/tex].

View image xero099
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